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agasfer [191]
3 years ago
11

The vertices of a triangle are labeled clockwise A(–5, 3), B(6, 1), and C(–2, –3). How could you show that the figure is a right

triangle?

Mathematics
1 answer:
mafiozo [28]3 years ago
5 0

Explanation:

When the points are plotted on a graph, it is easy to see that the slope of AC is -2 and the slope of BC is 1/2. These slope values have a product of -1, so the corresponding line segments are perpendicular to each other.

___

If you have studied vectors, you can find the dot product of AC with BC:

  AC = (-5, 3) -(-2, -3) = (-3, 6)

  BC = (6, 1) -(-2, -3) = (8, 4)

The dot product is ...

  (-3, 6)·(8, 4) = (-3)(8) + (6)(4) = -24+24 = 0

When the dot product of vectors is zero, they are perpendicular.

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3 0
3 years ago
Please help! What is the volume of the triangular pyramid?
vivado [14]

Answer:

30cm3

Step-by-step explanation:

Volume=Base area *height

Base area is a triangle=1/2 *base*height

1/2*3*4=6cm2

Height=5cm

Volume=6*5=30cm3

5 0
3 years ago
Read 2 more answers
A) x²y-2xy+y=? <br>b) ax²+4ax+4a=? <br>c) 20x-60x²+45x³=?​
bearhunter [10]

Answer:

A)Y(x²-2x+1)=y(x-1)²

B) a (x²+4 x+4)= a(x+2)²

C)x(20-60x+45x)²

hope I helped :)

5 0
3 years ago
Do you agree with the researchers method of predicting the population? Why or why not?
Burka [1]

Yes, I agree with the researcher's method. All the values of a_{n} in the table correspond to the values of n by using their formula.

Step-by-step explanation:

Step 1:

If we substitute the values of n in the researcher's equation and we get the right values of a_{n}, we can agree with the researcher's method.

The researcher's formula is a_{n} = 1000(2)^{n-1}. Here a_{n} is the wombat population and n is the number of years.

Step 2:

When n = 1, a_{1} = 1000(2)^{1-1} =  1000(1) = 1,000,

when n = 2, a_{2} = 1000(2)^{2-1} = 1000(2) = 2,000,

when n = 3, a_{3} = 1000(2)^{3-1} = 1000(4) = 4,000,

when n = 4, a_{4} = 1000(2)^{4-1} = 1000(8) = 8,000,

when n = 5, a_{5} = 1000(2)^{5-1} = 1000(16) = 16,000.

As all the values correspond to the values on the table, I agree with the researcher's method.

6 0
3 years ago
Multiply (2.0 ⋅ 10−4) ⋅ (3.1 ⋅ 10−20). Express the answer in scientific notation. The options are:
Mkey [24]
(2.0×10^-4)×(3.1×10^-20)
=(2.0×3.1)×(10^4×10^-20)
=6.2×10^(-4+(-20))
=6.2×10^-24. Hope it help!
3 0
3 years ago
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